Breathing Black Hole Shadows in Modified Gravity (MOG)

TL;DR

This paper explores how modified gravity (MOG) introduces unique, observable signatures in black hole shadows, such as breathing modes and shadow wobbling, which can be tested with future interferometry to detect additional gravitational fields.

Contribution

It demonstrates that MOG's scalar and vector fields produce distinct, time-dependent signatures in black hole shadows, breaking degeneracy with general relativity and providing new observational tests.

Findings

MOG scalar field causes a rhythmic expansion and contraction of the shadow area.

Massive MOG vector field leads to a delayed, wobbling shadow motion.

Distinct signatures can be used to test for extra gravitational fields in future observations.

Abstract

In this paper, we investigate the dynamic phenomenological signatures of a Schwarzschild-MOG black hole shadow perturbed by passing gravitational waves. By perturbing the Hamilton-Jacobi equation for photon null geodesics, we demonstrate that the unique field content of MOG breaks the observational degeneracy with standard General Relativity. We mathematically prove two distinct, time-dependent signatures. First, the massless MOG scalar field induces a volumetric ``breathing mode'' polarization, causing the total apparent area of the shadow to rhythmically expand and contract. Second, the massive MOG vector field undergoes quantum vacuum dispersion, arriving at the observer with a predictable time delay. This delayed massive wave sources secondary longitudinal metric perturbations that manifest as a sudden, asymmetric translational wobble of the shadow on the celestial screen. These dynamic geometric shifts offer a robust observational template for next-generation interferometry to strictly test the existence of massive force carriers and scalar fields in gravity.